Some recovery type error estimators for linear finite elements are analyzed under O(h 1+α ) (α > 0) regular grids. Superconvergence of order O(h 1+ρ ) (0 < p < α) is established for recovered gradients by three different methods. As a consequence, a posteriori error estimators based on those recovery methods are asymptotically exact.

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Analysis of recovery type a posteriori error estimators for mildly structured grids

Recovery procedures in error estimation and adaptivity Part I: Adaptivity in linear problems

Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes

We discuss, in this paper, a flux-free method for the computation of strict upper bounds of the energy norm of the error in a Finite Element (FE) computation. The bounds are strict in the sense that they refer to the difference between the displacement computed on the FE mesh and the exact displacement, solution of the continuous equations, rather than to the difference between the displacements computed on two FE meshes, one coarse and one refined. This method is based on the resolution of a series of local problems on patches of elements and does not require the resolution of a previous problem of flux equilibration, as happens with other methods. The paper concentrates more specifically on linear solid mechanics issues, and on the assessment of the energy norm of the error, seen as a necessary tool for the estimation of the error in arbitrary quantities of interest (linear functional outputs). Applications in both 2D and 3D are presented.

/pdf/strict-error-bounds-for-linear-solid-mechanics-problems-4umqo0ytia.pdf

J.Z. Zhu

Papers

A posteriori error estimation—the relationship between different procedures

The relationship of some a posteriori estimators